Problem Solving

VJesus12 wrote:Mary's income is 60 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income?

(A) 124%
(B) 120%
(C) 96%
(D) 80%
(E) 64%

[spoiler]OA=C[/spoiler]

Source: Official Guide

I suggest that we choose some nice values that meet the given conditions.

Tim's income is 40 percent less than Juan's income.
Let Juan's income = $100
40% of $100 = $40
This means Tim's income = $100 - $40 = $60

Mary's income is 60 percent more than Tim's income
60% of $60 = $36
So Mary's income = $60+ $36 = $96

What percent of Juan's income is Mary's income?
Juan's income = $100
Mary's income = $96

So, Mary's income is 96% of Juan's income
Answer: C

Cheers,
Brent

VJesus12 wrote:Mary's income is 60 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income?

(A) 124%
(B) 120%
(C) 96%
(D) 80%
(E) 64%

[spoiler]OA=C[/spoiler]

Source: Official Guide

To solve this problem we create variables for the income of Mary, Tim, and Juan, and then set up some equations.

T = Tim's income

M = Mary's income

J = Juan's income

We are given that Mary's income is 60% more than Tim's. Thus, we can say:

M = 1.6T

We are also given that Tim's income is 40% less than Juan's income. So we can say:

T = 0.6J

We are asked to determine the percent of Juan's income that Mary's income is. For this we can set up the expression:

M/J x 100%

To complete this problem we must express Juan's income and Mary's income in terms of a common variable. That common variable is T. Thus, we have:

M = 1.6T

J = T/0.6

So finally we can substitute T/0.6 for J and 1.6T for M

M/J x 100%

(1.6T)/(T/0.6) x 100%

(1.6T) x (0.6/T) x 100%

The T's cancel and we have:

1.6 x 0.6 x 100%

0.96 x 100% = 96%

Alternate Solution:

Let Tim's income be 100. Then Mary's income is 160 and Juan's income is 100/0.6 = 500/3 ≈ 166.6. We see that Mary's income is just slightly less than Juan's income and eyeballing the answer choices, we notice that 96% is the only possible answer.

Answer: C